If he took his parents to see Finding Nemo he was creating a self-fulfilling prophecy... Nemo's mom gets killed in the opening of the movie and his father gets taken away... did Lil' Bruce hate his parents???

Ace was a German Shepherd Dog originally owned by an engraver named John Wilker. He was found by Batman and Robin after his master was kidnapped by a gang of counterfeiters. Batman used Ace to try to locate Wilker. Because he had already placed a large number of "lost dog" announcements for Ace in his civilian identity of Bruce Wayne, he was concerned that anyone recognizing Ace (who had a prominent star-shaped marking on his forehead) might make the connection between Bruce Wayne and Batman. To forestall that problem, he hastily improvised a hood-like mask for the dog that incorporated the bat emblem as a dog tag dangling from Ace's collar. Ace was subsequently christened "The Bat-Hound" by a criminal he helped Batman to apprehend.

Having Batman's face exposed is possibly similar to why to he has a cape, at least in comic terms. A cape helped give the character a sense of motion within the static images of the comics' medium. Of course, his image was also inspired by the fact that the film Zorro had a cape. Having the lower part of his face exposed also allows the character to show expression which would be really hard or very limited to do if all you had were the eye slits visible. And again Zorro had his lower face exposed as well.

In real terms it's hard to imagine how a cowl made of fabric could be made or sculpted to form something of a scowl over the eyes as was done with Christian Bale's mask. Probably not impossible, but hard to imagine.

Having the lower face exposed could also be a seen as a means of expressing friendliness towards those not intended to fear Batman, such as innocent civilians and children.